In an interview on ABC's Lateline on Thursday night, Senator Xenophon compared the scheme to the Norwegian Blue parrot in the British comedy troupe's "dead parrot" sketch, in which a man returns a dead bird to a pet shop to complain, only to have the shop owner insist the animal is still alive.

"I think the paid parental leave scheme is a bit like that Monty Python's dead parrot," Senator Xenophon said.

"The government thinks it's alive, but it's well and truly gone."

Libertarian senator David Leyonhjelm, who was interviewed alongside Senator Xenophon, agreed: "Yes, it's a dead parrot. There's no way [it will survive] - unless the Greens support it, that's a possibility."

As the government continues to struggle to sell its budget three months after it was handed down by Treasurer Joe Hockey, Senator Xenophon said Prime Minister Tony Abbott's signature paid parental leave scheme was an example of where the government's message was falling short.

He said there were structural issues in the economy that the government should tackle in "a fair and systemic way" but that message did not sit well alongside the expensive scheme.

"The government has a tin ear when it comes to some of the issues facing Australians who are struggling out there ... who are worried about what the impact of the budget will be on them and we have an extravagant paid parental leave scheme, a Rolls Royce scheme, that seems to go against the government's message in respect of the age of entitlement," he said.

Earlier this month, Fairfax Media reported the $5.5 billion parental leave plan had been quietly shelved and would not be put to parliament this year amid disquiet from government backbenchers over what is seen as an overly generous scheme.

Opposition Leader Bill Shorten told ABC Radio on Friday the government should drop the scheme entirely.

"There's only one person who supports it and it's Tony Abbott," he said.

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